[Gen 9:13] this is basically saying whenever we see a rainbow. It's a sign of God's faithfulness and presence, right?

Not exactly. In Genesis 9:13, the rainbow is specifically the sign of God’s covenant with Noah and every living creature: God will never again destroy all life by a flood. It can remind Christians of God’s faithfulness, but the passage does not say that each rainbow signals God’s presence in a personal or newly delivered message. The surrounding covenant is about God’s promise after the flood, not a guarantee that hardship will not come. So the sound conclusion is that a rainbow recalls God’s covenant faithfulness, rather than serving as a private omen or direct message.